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Article Citation - WoS: 24Citation - Scopus: 24Symplectic and multisymplectic Lobatto methods for the "good" Boussinesq equation(Amer inst Physics, 2008) Aydin, A.; Karasoezen, B.In this paper, we construct second order symplectic and multisymplectic integrators for the "good" Boussineq equation using the two-stage Lobatto IIIA-IIIB partitioned Runge-Kutta method, which yield an explicit scheme and is equivalent to the classical central difference approximation to the second order spatial derivative. Numerical dispersion properties and the stability of both integrators are investigated. Numerical results for different solitary wave solutions confirm the excellent long time behavior of symplectic and multisymplectic integrators by preservink local and global energy and momentum. (C) 2008 American Institute of Physics.Conference Object Citation - WoS: 1Operator Splitting of the Kdv-Burgers Type Equation With Fast and Slow Dynamics(Amer inst Physics, 2010) Aydin, A.; Karasozen, B.The Korteweg de Vries-Burgers (KdV-Burgers) type equation arising from the discretization of the viscous Burgers equation with fast dispersion and slow diffusion is solved using operator splitting. The dispersive and diffusive parts are discretized in space by second order conservative finite differences. The resulting system of ordinary differential equations are composed using the time reversible Strang splitting. The numerical results reveal that the periodicity of the solutions and the invariants of the KdV-Burgers equation are well preserved.Article Citation - WoS: 17Citation - Scopus: 16Multisymplectic Box Schemes for the Complex Modified Korteweg-De Vries Equation(Amer inst Physics, 2010) Aydin, A.; Karasozen, B.In this paper, two multisymplectic integrators, an eight-point Preissman box scheme and a narrow box scheme, are considered for numerical integration of the complex modified Korteweg-de Vries equation. Energy and momentum preservation of both schemes and their dispersive properties are investigated. The performance of both methods is demonstrated through numerical tests on several solitary wave solutions. (C) 2010 American Institute of Physics. [doi:10.1063/1.3456068]Conference Object Citation - WoS: 1Multisymplectic Schemes for the Complex Modified Korteweg-De Vries Equation(Amer inst Physics, 2008) Aydin, A.; Karasoezen, B.In this paper, the multisymplectic formulation of the CMKdV(complex modified Korteweg-de Vries equation) is derived. Based on the multisymplectic formulation, the eight-point multisymplectic Preissman scheme and a linear-nonlinear multisymplectic splitting scheme are developed. Both methods are compared numerically with respect to the conservation of local and global quantities of the CMKdV equation.
